Question

1)The current spot price is $100. You observe 90 Calls selling for $5 and 110 Puts selling

for $5. Is there an arbitrage possibility? If so, how would you take advantage of it? What

are your potential profits?

2)The current spot price is $100. You observe ATM Calls selling for $10 and ATM Puts

selling for $7. Does Put-Call Parity hold?

a.Given the call price, how much should a put sell for?

b.Given the put price, how much should a call sell for?

3)Suppose the current s

pot price of an asset is $100. The current interest rate is 5%. The

underlying asset can go up by 10% or down by 10%. Using a 1-period Binomial Model,

how much should an ATM Call (strike = 100) sell for?

4)Suppose the current spot price of an asset is $100

The current interest rate is 3%. The underlying asset can go up by 5% or down by 3%. Using a 1 -period Binomial Model, how much should an ATM Call (strike = 100) sell for? What about an OTM Call (strike = 101)?

Or an ITM Call (strike = 95)?

Answer 1

1]

Yes, there is an arbitrage possibility.

An arbitrage profit can be earned by these steps :

Call options

• Buy the 90 call option for $5
• Exercise the option and buy the stock at $90
• Sell the stock at the market price of $100
• Arbitrage profit = sale price of stock - purchase price of stock - premium paid
• Arbitrage profit = $100 - $90 - $5 = $5

Put options

• Buy the 110 put option for $5
• Buy the stock at the market price of $100
• Exercise the option and sell the stock at $110
• Arbitrage profit = sale price of stock - purchase price of stock - premium paid
• Arbitrage profit = $110 - $100 - $5 = $5